Subgroups — #34058867

Order 19072.

1060 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750371	C₂	1	2	yes	maximal, complemented
2	#23750365	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750359	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750326	C₂	1	2	yes	maximal, complemented
5	#23750307	C₂	1	2	yes	maximal, complemented
6	#23750305	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750300	C₂	1	2	yes	maximal, complemented
8	#23750278	C₂	1	2	yes	maximal, complemented
9	#23750266	C₂	1	2	yes	maximal, complemented
10	#23750249	C₂	1	2	yes	maximal, complemented
11	#23750231	C₂	1	2	yes	maximal, complemented
12	#23750221	C₂	1	2	yes	maximal, complemented
13	#23750214	C₂	1	2	yes	maximal, complemented
14	#23750214	C₂	1	2	yes	maximal, complemented
15	#23750193	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750186	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750138	C₂	1	2	yes	maximal, complemented
18	#123×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#563×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14558737	C₂²	1	2	yes	—
21	C₂×#14558737	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
25	#18011908	C₂²	1	1	yes	characteristic, complemented
26	#18011907	C₂²	1	1	yes	characteristic
27	#18011906	C₂²	1	2	yes	complemented
28	#18011906	C₂²	1	2	yes	complemented
29	#18011906	C₂²	1	2	yes	complemented
30	#18011904	C₂²	1	2	yes	complemented
31	#18011901	C₂²	1	2	yes	complemented
32	#18011901	C₂²	1	2	yes	complemented
33	#18011900	C₂²	1	1	yes	characteristic, complemented
34	#18011900	C₂²	1	2	yes	complemented
35	#18011899	C₂²	1	2	yes	complemented
36	#18011897	C₂²	1	2	yes	complemented
37	#18011897	C₂²	1	2	yes	complemented
38	#18011896	C₂²	1	2	yes	—
39	#18011896	C₂²	1	2	yes	—
40	#18011896	C₂²	1	2	yes	complemented
41	#18011896	C₂²	1	2	yes	complemented
42	#18011896	C₂²	1	2	yes	complemented
43	#18011896	C₂²	1	2	yes	complemented
44	#18011896	C₂²	1	2	yes	complemented
45	#18011896	C₂²	1	2	yes	complemented
46	#18011896	C₂²	1	2	yes	complemented
47	#18011895	C₂²	1	1	yes	characteristic, complemented
48	#18011894	C₂²	1	1	yes	characteristic
49	#18011894	C₂²	1	1	yes	characteristic, complemented
50	#18011893	C₂²	1	2	yes	—
51	#18011893	C₂²	1	2	yes	complemented
52	#18011893	C₂²	1	2	yes	complemented
53	#18011892	C₂²	1	1	yes	characteristic
54	#18011891	C₂²	1	2	yes	complemented
55	#18011889	C₂²	1	2	yes	complemented
56	#18011889	C₂²	1	2	yes	complemented
57	#18011887	C₂²	1	2	yes	complemented
58	#18011887	C₂²	1	2	yes	complemented
59	#18011887	C₂²	1	2	yes	complemented
60	#18011886	C₂²	1	2	yes	—
61	#18011886	C₂²	1	2	yes	—
62	#18011886	C₂²	1	2	yes	complemented
63	#18011886	C₂²	1	2	yes	complemented
64	#18011886	C₂²	1	2	yes	complemented
65	#18011886	C₂²	1	2	yes	complemented
66	#18011886	C₂²	1	2	yes	complemented
67	#18011885	C₂²	1	2	yes	complemented
68	#18011884	C₂²	1	2	yes	—
69	#18011884	C₂²	1	2	yes	—
70	#18011884	C₂²	1	2	yes	complemented
71	#18011884	C₂²	1	2	yes	complemented
72	#18011881	C₂²	1	1	yes	characteristic
73	#18011881	C₂²	1	2	yes	—
74	#18011881	C₂²	1	2	yes	—
75	#18011881	C₂²	1	2	yes	complemented
76	#18011881	C₂²	1	2	yes	complemented
77	#18011879	C₂²	1	1	yes	characteristic
78	#18011876	C₂²	1	2	yes	complemented
79	C₄×D₅₉₆	C₂²	1	2	yes	complemented
80	C₄×D₅₉₆	C₂²	1	2	yes	complemented
81	#18011873	C₂²	1	2	yes	—
82	#18011873	C₂²	1	2	yes	complemented
83	#18011873	C₂²	1	2	yes	complemented
84	#18011873	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
86	#18011871	C₂²	1	2	yes	complemented
87	#18011871	C₂²	1	2	yes	complemented
88	#18011869	C₂²	1	2	yes	complemented
89	#18011868	C₂²	1	1	yes	characteristic, complemented
90	#18011868	C₂²	1	2	yes	complemented
91	#18011868	C₂²	1	2	yes	complemented
92	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
93	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
95	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
97	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
98	C₄⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
99	#126×C₁₄₉	C₂²	1	2	yes	complemented
100	#126×C₁₄₉	C₂²	1	2	yes	complemented
101	#125×C₁₄₉	C₂²	1	2	yes	complemented
102	#124×C₁₄₉	C₂²	1	1	yes	characteristic
103	#123×C₁₄₉	C₂²	1	1	yes	characteristic
104	#123×C₁₄₉	C₂²	1	1	yes	characteristic
105	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
106	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
107	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
108	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
109	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
110	#14558737	—	4	4	no	—
111	#14558737	—	4	2	no	—
112	C₂×Dic₂₉₈	C₂³	1	2	yes	—
113	C₂×D₅₉₆	—	4	2	no	—
114	C₂×D₅₉₆	C₂³	1	2	yes	—
115	C₂×D₅₉₆	C₂³	1	2	yes	—
116	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
117	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
118	C₂×D₅₉₆	C₂³	1	2	yes	—
119	C₂×D₅₉₆	C₂³	1	2	yes	—
120	C₂×D₅₉₆	C₂³	1	2	yes	—
121	C₂×D₅₉₆	C₂³	1	2	yes	—
122	C₂×D₅₉₆	C₂³	1	2	yes	—
123	C₂×D₅₉₆	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
129	D₄×D₁₄₉	—	4	2	no	—
130	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₁₄₉	—	4	2	no	—
132	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
133	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
135	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
136	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
137	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
138	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
139	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
140	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
141	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
142	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
143	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
144	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
145	#14558715	C₂³	1	2	yes	—
146	#14558715	C₂³	1	2	yes	—
147	#14558715	C₂³	1	2	yes	—
148	#14558715	C₂³	1	2	yes	—
149	#14558715	C₂³	1	2	yes	—
150	#14558715	C₂³	1	2	yes	—
151	#14558715	C₂³	1	2	yes	—
152	#14558715	C₂³	1	2	yes	—
153	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
154	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
156	#14558713	C₂³	1	2	yes	—
157	#14558713	C₂³	1	2	yes	—
158	#14558713	C₂³	1	2	yes	—
159	#14558713	C₂³	1	2	yes	—
160	#14558713	C₂³	1	2	yes	—
161	#14558713	C₂³	1	2	yes	—
162	#14558713	C₂³	1	2	yes	—
163	#14558713	C₂³	1	2	yes	—
164	#14558713	C₂³	1	2	yes	—
165	#14558713	C₂³	1	2	yes	—
166	#14558713	C₂³	1	2	yes	—
167	#14558713	C₂³	1	2	yes	—
168	#14558713	C₂³	1	2	yes	—
169	#14558713	C₂³	1	2	yes	—
170	#14558713	C₂³	1	2	yes	—
171	#14558713	C₂³	1	2	yes	—
172	#14558713	C₂³	1	2	yes	—
173	#14558713	C₂³	1	2	yes	—
174	C₄×Dic₁₄₉	C₂³	1	2	yes	—
175	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
176	C₄×Dic₁₄₉	C₂³	1	2	yes	—
177	C₄×Dic₁₄₉	C₂³	1	2	yes	—
178	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
179	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
181	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
182	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
183	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
184	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
185	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
186	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
187	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
188	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
190	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
196	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
197	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
198	C₄²×C₁₄₉	C₂³	1	2	yes	—
199	C₂²×D₁₄₉	—	2	2	no	—
200	C₂²×D₁₄₉	—	2	2	no	—
201	C₂²×D₁₄₉	—	4	2	no	—
202	C₂²×D₁₄₉	—	4	1	no	—
203	C₂²×D₁₄₉	—	4	2	no	—
204	C₂²×D₁₄₉	—	4	2	no	—
205	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
206	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
207	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
208	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
209	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
210	Dic₂₉₈	—	4	2	no	—
211	D₅₉₆	—	2	4	no	—
212	D₅₉₆	—	2	4	no	—
213	D₅₉₆	—	4	1	no	—
214	D₅₉₆	—	4	2	no	—
215	D₅₉₆	—	4	2	no	—
216	D₅₉₆	—	4	2	no	—
217	D₅₉₆	—	4	2	no	—
218	D₅₉₆	—	4	2	no	—
219	D₅₉₆	—	4	2	no	—
220	D₅₉₆	—	4	1	no	—
221	C₂²⋊D₁₄₉	—	4	1	no	—
222	C₂²⋊D₁₄₉	—	4	1	no	—
223	C₂²⋊D₁₄₉	—	4	2	no	—
224	C₂²⋊D₁₄₉	—	4	2	no	—
225	C₂²⋊D₁₄₉	—	4	2	no	—
226	C₂×Dic₁₄₉	—	4	1	no	—
227	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
228	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
229	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
230	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
231	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
232	C₄×D₁₄₉	—	2	4	no	—
233	C₄×D₁₄₉	—	2	2	no	—
234	C₄×D₁₄₉	—	4	2	no	—
235	C₄×D₁₄₉	—	4	2	no	—
236	C₄×D₁₄₉	—	4	2	no	—
237	C₄×D₁₄₉	—	4	2	no	—
238	C₄×D₁₄₉	—	4	2	no	—
239	C₄×D₁₄₉	—	4	2	no	—
240	C₄×D₁₄₉	—	4	2	no	—
241	C₄×D₁₄₉	—	4	2	no	—
242	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
243	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
244	Q₈×C₁₄₉	—	4	2	no	—
245	Q₈×C₁₄₉	—	4	1	no	—
246	D₄×C₁₄₉	—	4	1	no	—
247	C₂×C₄×C₁₄₉	—	4	1	no	—
248	C₂×C₄×C₁₄₉	—	4	1	no	—
249	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
256	C₂²×C₁₄₉	—	2	1	no	—
257	C₂²×C₁₄₉	—	2	1	no	—
258	C₂²×C₁₄₉	—	2	2	no	—
259	C₂²×C₁₄₉	—	2	2	no	—
260	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
261	C₂×D₁₄₉	—	2	2	no	—
262	C₂×D₁₄₉	—	2	1	no	—
263	C₂×D₁₄₉	—	2	2	no	—
264	C₂×D₁₄₉	—	2	2	no	—
265	C₂×D₁₄₉	—	2	1	no	—
266	C₂×D₁₄₉	—	2	2	no	—
267	C₂×D₁₄₉	—	2	2	no	—
268	C₂×D₁₄₉	—	2	2	no	—
269	C₂×D₁₄₉	—	2	2	no	—
270	C₂×D₁₄₉	—	2	2	no	—
271	C₂×D₁₄₉	—	2	2	no	—
272	C₂×D₁₄₉	—	4	4	no	—
273	C₂×D₁₄₉	—	8	2	no	—
274	C₂×D₁₄₉	—	8	2	no	—
275	C₂×D₁₄₉	H(5,𝔽₂)	1	2	yes	—
276	C₄×C₁₄₉	—	2	2	no	—
277	C₄×C₁₄₉	—	2	2	no	—
278	C₄×C₁₄₉	—	2	1	no	—
279	C₄×C₁₄₉	—	2	2	no	—
280	C₄×C₁₄₉	—	2	2	no	—
281	C₄×C₁₄₉	—	2	2	no	—
282	C₄×C₁₄₉	—	2	2	no	—
283	Dic₁₄₉	—	2	2	no	—
284	Dic₁₄₉	—	2	1	no	—
285	Dic₁₄₉	—	2	2	no	—
286	Dic₁₄₉	—	2	2	no	—
287	Dic₁₄₉	—	2	2	no	—
288	C₂×C₁₄₉	—	4	1	no	—
289	C₂×C₁₄₉	—	4	1	no	—
290	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₁₄₉	#585	1	2	yes	—
292	D₁₄₉	—	2	2	no	—
293	D₁₄₉	—	4	2	no	—
294	D₁₄₉	—	4	1	no	—
295	D₁₄₉	—	4	2	no	—
296	D₁₄₉	—	4	1	no	—
297	C₁₄₉	#3533	1	1	yes	characteristic, complemented, Sylow
298	#3533	—	149	1	no	maximal, Sylow
299	#563	D₁₄₉	1	1	yes	characteristic, complemented
300	#562	—	149	2	no	—
301	#560	—	149	1	no	—
302	#559	—	149	1	no	—
303	#553	—	149	2	no	—
304	#552	—	149	2	no	—
305	#551	—	149	2	no	—
306	#551	—	149	1	no	—
307	#547	—	149	2	no	—
308	#546	—	149	2	no	—
309	#542	—	149	2	no	—
310	#540	—	149	2	no	—
311	#539	—	149	2	no	—
312	#538	—	149	2	no	—
313	#538	—	149	2	no	—
314	#535	—	149	1	no	—
315	#534	—	149	1	no	—
316	#525	—	149	2	no	—
317	C₂×#123	—	149	1	no	—
318	C₂×#41	—	149	2	no	—
319	C₂×#41	—	149	1	no	—
320	C₂²×D₄	—	149	1	no	—
321	C₂²×D₄	—	149	1	no	—
322	C₂³×C₄	—	149	1	no	—
323	C₄⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
324	#127	—	149	1	no	—
325	#127	—	149	1	no	—
326	#126	—	149	2	no	—
327	#126	—	149	2	no	—
328	#126	—	149	2	no	—
329	#126	—	149	2	no	—
330	#126	C₂×D₁₄₉	1	2	yes	complemented
331	#126	C₂×D₁₄₉	1	2	yes	complemented
332	#125	—	149	2	no	—
333	#125	—	149	2	no	—
334	#125	C₂×D₁₄₉	1	2	yes	complemented
335	#124	—	149	1	no	—
336	#124	—	149	2	no	—
337	#124	—	149	2	no	—
338	#124	—	149	2	no	—
339	#124	—	149	2	no	—
340	#124	C₂×D₁₄₉	1	1	yes	characteristic
341	#123	—	149	1	no	—
342	#123	—	149	1	no	—
343	#123	—	149	1	no	—
344	#123	—	149	2	no	—
345	#123	—	149	2	no	—
346	#123	—	149	2	no	—
347	#123	—	149	2	no	—
348	#123	—	149	2	no	—
349	#123	—	149	2	no	—
350	#123	—	149	2	no	—
351	#123	—	149	2	no	—
352	#123	—	149	2	no	—
353	#123	—	149	2	no	—
354	#123	—	149	1	no	—
355	#123	—	149	2	no	—
356	#123	—	149	2	no	—
357	#123	C₂×D₁₄₉	1	1	yes	characteristic
358	#123	C₂×D₁₄₉	1	1	yes	characteristic
359	C₂²⋊Q₈	—	149	2	no	—
360	C₂²⋊Q₈	—	149	2	no	—
361	C₂²⋊Q₈	—	149	2	no	—
362	C₂²⋊Q₈	—	149	2	no	—
363	C₂²⋊Q₈	—	149	2	no	—
364	C₂²⋊Q₈	—	149	2	no	—
365	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
366	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
367	#121	—	149	2	no	—
368	#121	—	149	2	no	—
369	#121	—	149	2	no	—
370	#121	—	149	2	no	—
371	#121	—	149	2	no	—
372	#121	—	149	2	no	—
373	#121	—	149	2	no	—
374	#121	—	149	2	no	—
375	#121	—	149	2	no	—
376	#121	—	149	2	no	—
377	#121	—	149	2	no	—
378	#121	—	149	2	no	—
379	#120	—	149	1	no	—
380	#120	—	149	2	no	—
381	#120	—	149	2	no	—
382	#120	—	149	1	no	—
383	#120	—	149	2	no	—
384	#120	—	149	2	no	—
385	C₄×Q₈	—	149	2	no	—
386	C₄×D₄	—	149	2	no	—
387	C₄×D₄	—	149	2	no	—
388	C₄×D₄	—	149	2	no	—
389	C₄×D₄	—	149	2	no	—
390	C₄×D₄	—	149	2	no	—
391	C₄×D₄	—	149	2	no	—
392	C₄×D₄	—	149	2	no	—
393	C₄×D₄	—	149	2	no	—
394	C₄×D₄	—	149	2	no	—
395	#117	—	149	2	no	—
396	#117	—	149	1	no	—
397	#117	—	149	2	no	—
398	#117	—	149	2	no	—
399	C₂×C₄⋊C₄	—	149	2	no	—
400	C₂×C₄⋊C₄	—	149	2	no	—
401	C₂×C₂²⋊C₄	—	149	1	no	—
402	C₂×C₂²⋊C₄	—	149	2	no	—
403	C₂×C₂²⋊C₄	—	149	1	no	—
404	C₂×C₂²⋊C₄	—	149	2	no	—
405	C₂⁴	—	149	1	no	—
406	C₂⁴	—	149	1	no	—
407	C₂⁴	—	149	1	no	—
408	#41	—	596	4	no	—
409	#41	—	596	2	no	—
410	C₂×Q₈	—	149	2	no	—
411	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
412	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
413	C₂×D₄	—	596	2	no	—
414	C₂×D₄	—	596	2	no	—
415	C₂×D₄	—	149	2	no	—
416	C₂×D₄	—	149	2	no	—
417	C₂×D₄	—	149	2	no	—
418	C₂×D₄	—	149	1	no	—
419	C₂×D₄	—	149	1	no	—
420	C₂×D₄	—	149	2	no	—
421	C₂×D₄	—	149	2	no	—
422	C₂×D₄	—	149	2	no	—
423	C₂×D₄	—	149	2	no	—
424	C₂×D₄	—	149	2	no	—
425	C₂×D₄	—	149	2	no	—
426	C₂×D₄	—	149	2	no	—
427	C₂×D₄	—	149	2	no	—
428	C₂×D₄	—	149	1	no	—
429	C₂×D₄	—	149	1	no	—
430	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
431	C₂²×C₄	—	596	2	no	—
432	C₂²×C₄	—	149	2	no	—
433	C₂²×C₄	—	149	1	no	—
434	C₂²×C₄	—	149	1	no	—
435	C₂²×C₄	—	149	2	no	—
436	C₂²×C₄	—	149	2	no	—
437	C₂²×C₄	—	149	2	no	—
438	C₂²×C₄	—	149	2	no	—
439	C₂²×C₄	—	149	2	no	—
440	C₂²×C₄	—	149	2	no	—
441	C₂²×C₄	—	149	2	no	—
442	C₂²×C₄	—	149	2	no	—
443	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
444	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
445	C₄⋊C₄	—	149	2	no	—
446	C₄⋊C₄	—	149	2	no	—
447	C₄⋊C₄	—	149	2	no	—
448	C₄⋊C₄	—	149	2	no	—
449	C₄⋊C₄	—	149	2	no	—
450	C₄⋊C₄	—	149	2	no	—
451	C₄⋊C₄	—	149	2	no	—
452	C₄⋊C₄	—	149	2	no	—
453	C₄⋊C₄	—	149	2	no	—
454	C₄⋊C₄	—	149	2	no	—
455	C₄⋊C₄	—	149	2	no	—
456	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
457	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
458	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
459	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
460	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
461	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
462	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
463	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
464	C₂²⋊C₄	—	149	2	no	—
465	C₂²⋊C₄	—	149	1	no	—
466	C₂²⋊C₄	—	149	1	no	—
467	C₂²⋊C₄	—	149	2	no	—
468	C₂²⋊C₄	—	149	2	no	—
469	C₂²⋊C₄	—	149	2	no	—
470	C₂²⋊C₄	—	149	2	no	—
471	C₂²⋊C₄	—	149	2	no	—
472	C₂²⋊C₄	—	149	2	no	—
473	C₂²⋊C₄	—	149	2	no	—
474	C₂²⋊C₄	—	149	2	no	—
475	C₂²⋊C₄	—	149	2	no	—
476	C₂²⋊C₄	—	149	2	no	—
477	C₂²⋊C₄	—	149	2	no	—
478	C₂²⋊C₄	—	149	2	no	—
479	C₂²⋊C₄	—	149	2	no	—
480	C₂²⋊C₄	—	149	2	no	—
481	C₂²⋊C₄	—	149	2	no	—
482	C₂²⋊C₄	—	149	2	no	—
483	C₂²⋊C₄	—	149	2	no	—
484	C₂²⋊C₄	—	149	2	no	—
485	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
487	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
488	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
489	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
491	C₄²	—	149	2	no	—
492	C₄²	—	149	2	no	—
493	C₄²	—	149	1	no	—
494	C₄²	—	149	2	no	—
495	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
496	C₄²	C₂²×D₁₄₉	1	2	yes	—
497	C₂³	—	298	2	no	—
498	C₂³	—	298	2	no	—
499	C₂³	—	596	2	no	—
500	C₂³	—	596	1	no	—
501	C₂³	—	596	2	no	—
502	C₂³	—	596	2	no	—
503	C₂³	—	149	1	no	—
504	C₂³	—	149	2	no	—
505	C₂³	—	149	1	no	—
506	C₂³	—	149	2	no	—
507	C₂³	—	149	1	no	—
508	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
509	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
510	Q₈	—	4	2	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	596	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	298	4	no	—
515	D₄	—	298	4	no	—
516	D₄	—	596	2	no	—
517	D₄	—	596	1	no	—
518	D₄	—	596	2	no	—
519	D₄	—	596	2	no	—
520	D₄	—	596	2	no	—
521	D₄	—	596	2	no	—
522	D₄	—	596	2	no	—
523	D₄	—	596	1	no	—
524	D₄	—	596	1	no	—
525	D₄	—	596	1	no	—
526	D₄	—	596	2	no	—
527	D₄	—	596	2	no	—
528	D₄	—	596	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	298	4	no	—
532	C₂×C₄	—	298	2	no	—
533	C₂×C₄	—	596	2	no	—
534	C₂×C₄	—	596	2	no	—
535	C₂×C₄	—	596	2	no	—
536	C₂×C₄	—	596	2	no	—
537	C₂×C₄	—	596	2	no	—
538	C₂×C₄	—	596	2	no	—
539	C₂×C₄	—	596	2	no	—
540	C₂×C₄	—	596	2	no	—
541	C₂×C₄	—	596	1	no	—
542	C₂×C₄	—	149	2	no	—
543	C₂×C₄	—	149	2	no	—
544	C₂×C₄	—	149	2	no	—
545	C₂×C₄	—	149	2	no	—
546	C₂×C₄	—	149	1	no	—
547	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
548	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
549	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
550	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
551	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
552	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
553	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	298	2	no	—
559	C₂²	—	298	2	no	—
560	C₂²	—	298	1	no	—
561	C₂²	—	298	2	no	—
562	C₂²	—	298	1	no	—
563	C₂²	—	298	2	no	—
564	C₂²	—	298	2	no	—
565	C₂²	—	298	2	no	—
566	C₂²	—	298	2	no	—
567	C₂²	—	298	2	no	—
568	C₂²	—	298	2	no	—
569	C₂²	—	596	4	no	—
570	C₂²	—	149	2	no	—
571	C₂²	—	1192	2	no	—
572	C₂²	—	1192	2	no	—
573	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	298	2	no	—
582	C₄	—	298	1	no	—
583	C₄	—	298	2	no	—
584	C₄	—	298	2	no	—
585	C₄	—	298	2	no	—
586	C₂	—	4	1	no	—
587	C₂	—	4	1	no	—
588	C₂	—	298	2	no	—
589	C₂	—	596	1	no	—
590	C₂	—	596	2	no	—
591	C₂	—	596	1	no	—
592	C₂	—	596	2	no	—
593	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
594	C₂	#23750462	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#563×C₁₄₉	C₂
hypercenter	#563	D₁₄₉
hypocenter	C₁₄₉	#3533
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #563

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #23750371	C₂	semidirect
2. #23750365	C₂	semidirect
3. #23750359	C₂	semidirect
4. #23750326	C₂	semidirect
5. #23750307	C₂	semidirect
6. #23750305	C₂	semidirect
7. #23750300	C₂	semidirect
8. #23750278	C₂	semidirect
9. #23750266	C₂	semidirect
10. #23750249	C₂	semidirect
11. #23750231	C₂	semidirect
12. #23750221	C₂	semidirect
13. #23750214	C₂	semidirect
14. #23750214	C₂	semidirect
15. #23750193	C₂	semidirect
16. #23750186	C₂	semidirect
17. #23750138	C₂	semidirect
18. #123×D₁₄₉	C₂	semidirect
19. #563×C₁₄₉	C₂	semidirect
21. C₂×#14558737	C₂²	semidirect
24. C₂²×C₄×D₁₄₉	C₂²	semidirect
25. #18011908	C₂²	semidirect
27. #18011906	C₂²	semidirect
28. #18011906	C₂²	semidirect
29. #18011906	C₂²	semidirect
30. #18011904	C₂²	semidirect
31. #18011901	C₂²	semidirect
32. #18011901	C₂²	semidirect
33. #18011900	C₂²	semidirect
34. #18011900	C₂²	semidirect
35. #18011899	C₂²	semidirect
36. #18011897	C₂²	semidirect
37. #18011897	C₂²	semidirect
40. #18011896	C₂²	semidirect
41. #18011896	C₂²	semidirect
42. #18011896	C₂²	semidirect
43. #18011896	C₂²	semidirect
44. #18011896	C₂²	semidirect
45. #18011896	C₂²	semidirect
46. #18011896	C₂²	semidirect
47. #18011895	C₂²	semidirect
49. #18011894	C₂²	semidirect
51. #18011893	C₂²	semidirect
52. #18011893	C₂²	semidirect
54. #18011891	C₂²	semidirect
55. #18011889	C₂²	semidirect
56. #18011889	C₂²	semidirect
57. #18011887	C₂²	semidirect
58. #18011887	C₂²	semidirect
59. #18011887	C₂²	semidirect
62. #18011886	C₂²	semidirect
63. #18011886	C₂²	semidirect
64. #18011886	C₂²	semidirect
65. #18011886	C₂²	semidirect
66. #18011886	C₂²	semidirect
67. #18011885	C₂²	semidirect
70. #18011884	C₂²	semidirect
71. #18011884	C₂²	semidirect
75. #18011881	C₂²	semidirect
76. #18011881	C₂²	semidirect
78. #18011876	C₂²	semidirect
79. C₄×D₅₉₆	C₂²	semidirect
80. C₄×D₅₉₆	C₂²	semidirect
82. #18011873	C₂²	semidirect
83. #18011873	C₂²	semidirect
84. #18011873	C₂²	semidirect
85. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
86. #18011871	C₂²	semidirect
87. #18011871	C₂²	semidirect
88. #18011869	C₂²	semidirect
89. #18011868	C₂²	semidirect
90. #18011868	C₂²	semidirect
91. #18011868	C₂²	semidirect
92. C₄⋊C₄×D₁₄₉	C₂²	semidirect
93. C₄⋊C₄×D₁₄₉	C₂²	semidirect
96. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
97. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
98. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
99. #126×C₁₄₉	C₂²	semidirect
100. #126×C₁₄₉	C₂²	semidirect
101. #125×C₁₄₉	C₂²	semidirect
105. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
106. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
297. C₁₄₉	#3533	semidirect
299. #563	D₁₄₉	semidirect
323. C₄⋊Q₈	C₂×D₁₄₉	semidirect
330. #126	C₂×D₁₄₉	semidirect
331. #126	C₂×D₁₄₉	semidirect
334. #125	C₂×D₁₄₉	semidirect
365. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
366. C₂²⋊Q₈	C₂×D₁₄₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23750371	2
#23750365	2
#23750359	2
#23750326	2
#23750307	2
#23750305	2
#23750300	2
#23750278	2
#23750266	2
#23750249	2
#23750231	2
#23750221	2
#23750214	2
#23750193	2
#23750186	2
#23750138	2
#123×D₁₄₉	2
#563×C₁₄₉	2
#3533	149